Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
784 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11752631 | C2 | semidirect |
| 3. #11750808 | C2 | semidirect |
| 4. C5×#4703 | C2 | semidirect |
| 5. C3×#65002 | C2 | semidirect |
| 6. #11748142 | C2 | semidirect |
| 7. #11747978 | C2 | semidirect |
| 8. #11746928 | C2 | semidirect |
| 9. #11746897 | C2 | semidirect |
| 40. #65002 | D3 | semidirect |
| 74. #4703 | D5 | semidirect |
| 305. C3×C5 | #3142 | semidirect |
| 345. C5 | #81716 | semidirect |
| 358. C3 | #10613471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752631 | 2 |
| #11752556 | 2 |
| #11750808 | 2 |
| C5×#4703 | 2 |
| C3×#65002 | 2 |
| #11748142 | 2 |
| #11747978 | 2 |
| #11746928 | 2 |
| #11746897 | 2 |
| #10613471 | 3 |
| #81716 | 5 |